EVENT DETAILS AND ABSTRACT

Title: Arithmetic Resurgence in Quantum Topology
Speaker: Stavros Garoufalidis
Speaker Info: Georgia Institute of Technology
Brief Description:
Special Note:
Abstract:

Quantum Topology assigns numerical invariants (such as the Jones polynomial) to knotted 3-dimensional objects. The asymptotic expansions of these invariants are conjecturally related to riemannian (and mostly hyperbolic) geometry in 3-dimensions. In our talk, we will repackage the quantum invariants to two power series, and formulate a precise Arithmetic Resurgence Conjecture regarding the position of the singularities and the structure of the local and global monodromy. Finally, we will give some proofs of our conjecture in some test cases, that include a series of Kontsevich-Zagier, and the Kashaev series of the simplest hyperbolic 4_1 knot. The second part is joint work with O. Costin.